1. Field of the Invention
The present invention relates to communication systems and, more particularly, to modulation of data-carrying signals.
2. Description of the Related Art
The capacity of communication systems is often limited by bandwidth and bandwidth utilization efficiency. In order to make more efficient use of any bandwidth available for use by a communication system, quadrature amplitude modulation (QAM) was developed. QAM is used in many advanced multiple access (MA) systems, including code division multiple access (CDMA), wideband CDMA (WCDMA), high-speed downlink packet access (HSPDA), evolution-data optimized (EV-DO), orthogonal frequency-division multiplexing (OFDM), worldwide interopability for microwave access (WiMAX), and long term evolution (LTE) systems. Different MA systems may use different orders of QAM, such as 2, 4, 16, 64 and 256, in which the QAM order indicates the number of different signals employed by the system. QAM uses two orthogonal Eigenfunctions, two sinusoids 90 degrees out of phase, within the same frequency band.
For example, conventional 64 QAM channel encoding and modulation uses eight discrete levels for each of the sinusoids. First, a stream of digital data with logical 0's and 1's is converted to two streams, an in-phase (I) and quadrature phase (Q) signal, each with discrete levels. Each data symbols in the I or Q stream represents three bits of the original digital data source. (23=8) Then, each symbol in each of the I and Q streams is modulated with a raised cosine filter to taper the signal, so that a time-domain waveform of the signal will be confined to the duration of the symbol. As a result, the footprints of the signals in the frequency domain will also be tapered to minimize interference with adjacent frequency channels. The I and Q signal streams are then converted to analog signals and used to modulate the in-phase (for example, cosine) and quadrature (for example, sine) components of a carrier signal. The modulated carrier components are summed to produce the 64 QAM signal, which may further be used to modulate a radio frequency (RF) signal.
To demodulate a 64 QAM signal, the RF signal is downconverted to baseband, for example, by using a quadrature down converter. The I and Q streams of baseband signal are digitized, and the energy of each symbol in the I and Q digital streams is determined by filtering and integrating over the symbol duration. The detected energy indicates the symbol value in each of the I or Q streams, which is then mapped into logical 0's and 1's. The digital data streams demodulated from the I and Q dimensions are multiplexed into a single stream to form the final demodulated digital data.
Prior to the advent of wavelet analysis techniques, communication theory was predominantly based on two methods of signal analysis. Signals were typically either modeled as functions of time at precisely defined at moments, or as functions of frequency, with ideal accuracy in frequency. Narrowband and wideband ambiguity functions, which enable representation of signals as both functions of time and frequency, are related to wavelet transforms. Wideband ambiguity functions are essentially affine wavelet transforms and narrowband ambiguity functions can be considered to be Heisenberg wavelet transforms. Wavelet transforms can be defined as time-frequency localization operators that treat the time-frequency plane as a notional two-dimensional space, rather than as two separate one-dimensional axes. In the case of narrowband ambiguity functions, time delayed and Doppler-shifted signals can be analyzed using a reference signal, g(t). Thus, a narrowband ambiguity function can be interpreted as a generalized Gabor transform of a received signal with respect to a reference signal. Gabor transforms have fundamental significance in physics and information theory, and may be referred to as the Heisenberg wavelet transform.